The aim of this reported work was investigation of a proper channel assignment method in the downlink channel of a multi-user wireless network in which the transmitter aims at sending individual data streams to certain numbers of users through a limited number of sub-channels. In this regard, considering the network throughput as the performance function, it is demonstrated that the problem can be formulated as an optimisation problem which is not convex in general. However, through relaxing some constraints, the problem can be cast as a convex optimisation problem, leading to a simple power allocation strategy.